When I do an amphibious with shore bombardment, can I take a hit on my battleship which comes from a land unit? Or can I only take the extra hit in seabattles?
You can't take hits on your sea units in the land battle.
And what about the destroyer that blocks Egypt. I know, when you pass an enemy vessel during an amphibious, you have to fight first and you lose the opening fire. The way we play, we send a separate german airforce to wipe away the destroyer first. Then, in the same turn, move into the Egypt seazone to start the amphibious WITH opening fire (because the BB wasn't in the seabattle). But I'm not sure if this is correct?
Nope, it's illegal. All combat movement must be complete before any combat is done (except for unloading of amphibious land units when a sea battle precedes the assault), so the ships will be in the sea zone and participate in the battle.
And one more thing, can you do the opening fire only once, or on every turn when you roll dice for your troops.
Only once per battle.